Hi everyone,
Thanks for your help. The problem was indeed that I needed to reboot the Virgin Media box (set into Modem mode) after connecting the Turris - the person who speculated that it only gives out one DHCP address was probably right. So now it’s all working nicely 
So for anyone else with this problem:
- Switch off the Omnia
- Unplug all Ethernet cables from your VM box except the Omnia (into the Modem mode port)
- Connect to VM box wifi or via Ethernet and use web interface to switch it to Modem mode
- Watch it reboot
- Wait until it has finished and the lights calm down
- Power on the Omnia
- Wait until it has fully booted
- Check that you can access the Internet via a cable plugged into the Omnia
Gerv